1. Identify the base and the exponent. A.6^3 B.2^3 C.(9)^5 - 8

The varsity basketball team started selling T-shirts online in 1994. The number of T-shirts sold online, s, is modeled by the gr

-Dominant- [34]

(PART-A): s-intercept in this case represents the y-intercept of the graph, whereas the t-intercept in this case represents the x-intercept of the graph.

Always remember that y-intercept represents the value of y where the curve (or line) crosses the y-axis, and x-intercept represents the value of x where the curve (or line) crosses the x-axis.

In the graph attached with the question, at point (0,6) the curve crosses the y-axis. Therefore, the y-intercept (s-intercept) in this case is 6. It means that in year 2000 (t=0), 6 hundred shirts were sold.

However, there is no point on the graph where the curve crosses the x-axis, meaning there is no x-intercept (t-intercept). It means that there is not a single year when the number of shirts sold is 0.

(PART B): As you can see in the graph (attached with the question) that the f(t) is increasing (exponentially) with the increase in t. Therefore, we can safely say that as t increases without bound, the f(t) increases (also). In this context, it means that the sale of shirts increases as the years go by. Hence, the correct blank is "increases."

(PART C): The average rate of change is actually the slope. To find the slope, we can use the following formula:

slope = $\frac{y_2 - y_1}{x_2 - x_1}$ --- (X)

Given points: (5, 12.5) and (7, 22). Plug the values in equation (X),

slope = $\frac{22-12.5}{7-5} = 4.75$

Hence, the average rate of change for the function between t=5 and t=7 is 4.75 (answer).

(PART D): This part is bit tricky. Therefore, read the explanation carefully!

You can see in the graph that number of Shirts sold is in hundreds. It means that 1 unit (of y-axis in a graph) represents 100 shirts. Therefore, as in the question it is mentioned that there are 1000 T-shirts sold, it will become 10 units (since 10*100 = 1000). So, the function g(t) will become the following:

$g(t) = f(t) + 10$ --- (Y)

Why did I add f(t)? Because in the question, the word "and" is underlined. It means that g(t) represents not only 1000 T-shirts (10*100 = 1000) sold at the basketball games each year, but it also has the number of T-shirts sold ONLINE, which is f(t).

Now insert f(t) in (Y) and solve:

$g(t) = f(t) + 10\\g(t) = (1.5)^t + 5+ 10\\g(t) = (1.5)^t + 15$

Hence, g(t) is $(1.5)^t + 15$

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3 years ago

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A first number plus twice a second number is 14. Twice the first number plus the second totals 10. Find the numbers.

Nookie1986 [14]

Answer:

first number(x) = 2 second number(y)= 6

Step-by-step explanation:

This is an example of a simultaneous equation.

First write this word problem as equations, where x is the "first number" that you've mentioned and y is the "second number".

x + 2y = 14 (equation 1)

2x + y = 10 (equation 2)

This is solved using the elimination method.

We need to make one of the coefficients the same - in this case we can make y the same. In order to do this we need to multiply equation 2 by 2, so that y becomes 2y.

2x + y = 10 MULTIPLY BY 2

4x + 2y = 20 (this is now our new equation 2 with the same y coefficient)

Now subtract equation 1 from equation 2.

4x - x + 2y - 2y = 20 - 14 (2y cancels out here)

3x = 6

x = 2

Now we substitute our x value into equation 1 to find the value of y.

2 + 2y = 14

2y = 12

y = 6

Hope this has answered your question.

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